MHB Graphical Problem with 1st and 2nd Derivaties

[Yankel]

Hello all,

I have a problem, in which the graph of the first derivative is given (forgive me for the x-axis scale, my drawing skills are not too good).

View attachment 6379

I need to tell, which of the points (on the x-axis) of the function itself, has the highest and lowest values, and which of the points of the second derivative function, has the highest and lowers values.

I know that when the first derivative is positive, the function f is increasing, and when it is negative, it is decreasing.

The derivative f'(x) is positive for every x in the graph, this means that f is increasing and therefore f(-5) is the lowest and f(5) is the highest.

I don't know how to solve the second derivative.

Can you please assist ?

Thank you !

 

[Yankel]

Is it correct to say that the max of f''(x) is at x=5 and the min of f''(x) is at x=0 ?

 

[MarkFL]

Is it correct to say that the max of f''(x) is at x=5 and the min of f''(x) is at x=0 ?

I would say, going by the graph, that:

$$f''_{\max}=f''(-5)$$

As that's where the slope of $f'$ seems to be the greatest. For $f''_{\min}$, you have to pick from the given choices, and I would choose $f''(1)$ as that's the only point given where the slope of $f'$ is negative.

For the first question, since $f'>0$ over the entire range then $f$ is increasing over that domain, so:

$$f_{\min}=f(-5)$$

$$f_{\max}=f(5)$$

 

[Yankel]

Thank you.